Stuck set screw in Moen shower faucet

I have a Moen shower faucet (don't know which model) that is a single handle faucet that rotates to turn on and mix the hot/cold water.

My wife called me at work and told me that the shower wouldn't turn off. When I got home I see that the plastic handle is really loose - it spins from the six o'clock position (off) to the nine o'clock (on full hot).

No problem I think, it's just the set screw has somehow come loose. However, then I take the cover off the plastic faucet head to get at the set screw and try to turn the set screw -- it turns but it turns the shower on, if I keep turning it gets to the point where the shower is turned off. In fact I can just keep turning the set screw in circles and the shower goes from on to off to on to off, etc.

So it appears as though the set screw is stuck in the cartridge (since it just keeps turning round and round).

I have no idea where to go from here...any ideas? If the set screw is indeed stuck (like I think) should the cartridge just continuously turn in circles like I mention?

Please help as we are not restricted to turn the shower on and off via the set screw with a Phillips screwdriver!!!

EDIT: So we have Moen faucets in the bathroom too. I just took the plastic handle off of one of those and see how the plastic faucet is molded on the inside to cover the cartridge and hold it in place (or actually turn the cartridge to turn the water on) when turning the set screw. Could this mean that the plastic inside my shower faucet is broken (thus not holding the cartridge in place while turning the set screw)? If so, any alternative than to try breaking the plastic (or cutting it) to get the handle off?

Sounds like a posi temp valve. The acrilyic handle is broken on the inside so no harm in breaking it off then hold the catridge stem with channel locks and remove the screw. Take the handle with you to a plumbing supplier and match it up and replace it.

The handle has the stop which limits the degree of rotation, so if it is broken then the stem can rotate, thus, you probably have to cut or break the handle off so you can hold the stem while removing the screw. Then you need a new handle.